Solution for Exercise 3.5 Monte Carlo integration

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    #| BEGIN (Write your solution here) |#
(define (random-in-range low high)
  (let ((range (- high low)))
    (+ low (random range))))

(define (monte-carlo trials experiment)
  (define (iter trials-remaining trials-passed)
    (cond ((= trials-remaining 0)
           (/ trials-passed trials))
          ((experiment)
           (iter (- trials-remaining 1) (+ trials-passed 1)))
          (else
           (iter (- trials-remaining 1) trials-passed))))
  (iter trials 0))


(define (circle-test)
  (let ((x (random-in-range -1.0 1.0))
        (y (random-in-range -1.0 1.0)))
    (<= (+ (* x x) (* y y)) 1.0)))

(define (estimate-integral trials)
  (* 4.0 (monte-carlo trials circle-test)))

#| END |#

    #| BEGIN (Write your solution here) |#
(define (square x) (* x x))

(define (in-circle? x y x0 y0 r)
  (<= (+ (square (- x x0)) (square (- y y0)))
      (square r)))

(define (estimate-integral predicate x1 x2 y1 y2 trials)
  (define (test)
    (let ((x (random-in-range x1 x2))
          (y (random-in-range y1 y2)))
      (predicate x y 0.0 0.0 1.0)))
  (* 4.0 (monte-carlo trials test)))
#| END |#

    #| BEGIN (Write your solution here) |#
(define (in-circle? x y)
  (<= (+ (square x) (square y)) 1.0))

(define (estimate-integral predicate x1 x2 y1 y2 trials)
  (define (test)
    (let ((x (random-in-range x1 x2))
          (y (random-in-range y1 y2)))
      (predicate x y)))
  (* 4.0 (monte-carlo trials test)))
#| END |#

    #| BEGIN (Write your solution here) |#
(define (random-in-range low high)
  (let ((range (- high low)))
    (+ low (random range))))

(define (monte-carlo trials experiment)
  (define (iter trials-remaining trials-passed)
    (cond ((= trials-remaining 0)
           (/ trials-passed trials))
          ((experiment)
           (iter (- trials-remaining 1) (+ trials-passed 1)))
          (else
           (iter (- trials-remaining 1) trials-passed))))
  (iter trials 0))


(define (circle-test)
  (let ((x (random-in-range -1.0 1.0))
        (y (random-in-range -1.0 1.0)))
    (<= (+ (* x x) (* y y)) 1.0)))

(define (estimate-integral trials)
  (* 4.0 (monte-carlo trials circle-test)))

#| END |#

    #| BEGIN (Write your solution here) |#
(define (square x) (* x x))

(define (in-circle? x y x0 y0 r)
  (<= (+ (square (- x x0)) (square (- y y0)))
      (square r)))

(define (estimate-integral predicate x1 x2 y1 y2 trials)
  (define (test)
    (let ((x (random-in-range x1 x2))
          (y (random-in-range y1 y2)))
      (predicate x y 0.0 0.0 1.0)))
  (* 4.0 (monte-carlo trials test)))
#| END |#

    #| BEGIN (Write your solution here) |#
(define (in-circle? x y)
  (<= (+ (square x) (square y)) 1.0))

(define (estimate-integral predicate x1 x2 y1 y2 trials)
  (define (test)
    (let ((x (random-in-range x1 x2))
          (y (random-in-range y1 y2)))
      (predicate x y)))
  (* 4.0 (monte-carlo trials test)))
#| END |#